NTA JEE Mains 2nd April Shift 2 2026

Let $$\alpha, \beta$$ be roots of the equation $$x^2 - 3x + r = 0$$, and $$\frac{\alpha}{2}, 2\beta$$ be roots of the equation $$x^2 + 3x + r = 0$$.
If roots of the equation $$x^2 + 6x = m$$ are $$2\alpha + \beta + 2r$$ and $$\alpha - 2\beta - \frac{r}{2}$$, then $$m$$ equals to :

Let the circles $$C_1 : |z| = r$$ and $$C_2 : |z - 3 - 4i| = 5$$, $$z \in \mathbb{C}$$, be such that $$C_2$$ lies within $$C_1$$. If $$z_1$$ moves on $$C_1$$, $$z_2$$ moves on $$C_2$$ and $$\min|z_1 - z_2| = 2$$, then $$\max|z_1 - z_2|$$ is equal to :

If the system of equations
$$x + 5y + 6z = 4$$,
$$2x + 3y + 4z = 7$$,
$$x + 6y + az = b$$
has infinitely many solutions, then the point $$(a, b)$$ lies on the line :

Let $$a_1, a_2, a_3, \ldots$$ be an A.P. and $$g_1 = a_1, g_2, g_3, \ldots$$ be an increasing G.P. If $$a_1 = a_2 + g_2 = 1$$ and $$a_3 + g_3 = 4$$, then $$a_{10} + g_5$$ is equal to :

The sum $$\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots$$ up to 8 terms, is :

If for $$3 \le r \le 30$$, $$\left({}^{30}C_{30-r}\right) + 3\left( ^{30}C_{31-r} \right) + 3\left( ^{30}C_{32-r}\right) + \left( ^{30}C_{33-r}\right) = {}^{m}C_r$$, then $$m$$ equals :

Let $$p_n$$ denote the total number of triangles formed by joining the vertices of an $$n$$-side regular polygon. If $$p_{n+1} - p_n = 66$$, then the sum of all distinct prime divisors of $$n$$ is :

A man throws a fair coin repeatedly. He gets 10 points for each head and 5 points for each tail he throws. If the probability that he gets exactly 30 points is $$\frac{m}{n}$$, $$\gcd(m, n) = 1$$, then $$m + n$$ is equal to :

The mean and variance of $$n$$ observations are 8 and 16, respectively. If the sum of the first $$(n-1)$$ observations is 48 and the sum of squares of the first $$(n-1)$$ observations is 496, then the value of $$n$$ is :

Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines $$x + (k-1)y + 3 = 0$$ and $$2x + k^2 y - 4 = 0$$. If the line $$x - y + 2 = 0$$ intersects the circle at the points $$A$$ and $$B$$, then $$(AB)^2$$ is equal to :